CATEGORIZING MODELS USING SELF-ORGANIZING MAPS: AN APPLICATION TO MODIFIED GRAVITY THEORIES PROBED BY COSMIC SHEAR

We propose to use Self-Organizing Maps (SOM) to map the impact of physical models onto observables. Using this approach, we are be able to determine how theories relate to each other given their signatures. In cosmology this will be particularly useful to determine cosmological models (such as dark energy, modified gravity or inflationary models) that should be tested by the new generation of experiments. As a first example, we apply this approach to the representation of a subset of the space of modified gravity theories probed by cosmic shear. We therefore train a SOM on shear correlation functions in the f(R), dilaton and symmetron models. The results indicate these three theories have similar signatures on shear for small values of their parameters but the dilaton has different signature for higher values. We also show that modified gravity (especially the dilaton model) has a different impact on cosmic shear compared to a dynamical dark energy so both need to be tested by galaxy surveys.

本文提出采用自组织映射（Self-Organizing Maps, SOM）将物理模型的影响映射至观测可观测量。借助该方法，我们能够基于理论的特征信号厘清不同理论间的关联。在宇宙学领域，该方法对于确定需由新一代实验开展检验的宇宙学模型（如暗能量（dark energy）、修正引力（modified gravity）或暴胀模型（inflationary models））具有重要应用价值。作为首个示例，我们将该方法应用于经宇宙剪切（cosmic shear）探测的修正引力理论空间子集的表征。具体而言，我们针对f(R)、伸缩子（dilaton）、对称子（symmetron）模型中的剪切相关函数（shear correlation functions）训练自组织映射。结果表明，当参数取值较小时，这三种理论在剪切信号上具有相似的特征；但伸缩子模型在参数取值较高时，其特征信号存在显著差异。此外，相较于动力学暗能量（dynamical dark energy）模型，修正引力（尤其是伸缩子模型）对宇宙剪切的影响存在明显区别，因此二者均需通过星系巡天（galaxy surveys）开展检验。